That's not at all atypical, and it's what you expect from a numerical
process to arrive at an eigenvector matrix. In the context of ones on
the main diagonal, 1e-16 is "mostly zero".
On 2015-06-22 03:08, Carrico, Paul wrote:
Dear Tim,
Thanks for the enlightenment, but unfortunately I confess I don't know
how to proceed now;
I feel that I need to fix such issue; another example if needed (see
screenshot in attachment), the product herebellow should lead to the
Identity matrix
Verif1 = u' * M * u
(vhere u is the eigenvector matrix)
Paul
-----Message d'origine-----
De : users [mailto:[email protected]] De la part de Tim
Wescott Envoyé : vendredi 19 juin 2015 18:38 À : International users
mailing list for Scilab.
Objet : Re: [Scilab-users] eigs calculation
"Normalization" refers to jiggering the numbers around in a way that
does not change the problem in a strictly mathematical sense, but
which makes it more tractable.
d = eigs(A, B) computes the solutions to
A * v = lambda * B * v
So any nonsingular square matrix N won't change the problem if it's
multiplied in:
N * A * v = N * lambda * B * v
Because lambda is a scalar (well, I hope I'm getting that right) you
can change the problem to
A_ = N * A, B_ = N * B, and
d = eigs(A_, B_)
will, theoretically, get the same answers as with the original
matrices, but possibly with better numerical conditioning. This is
what you're doing when you change units.
If you don't mind the meaning of your eigenvectors changing, you can
do a similarity transform. Start with
N * A * N^(-1) * N * v = N * lambda * B * N^(-1) * N * v
Now set
A_ = N * A * N^(-1)
B_ = N * B * N^(-1)
v_ = N * v
[d, v_] = eigs(A_, B_); v = N^(-1) * v_;
will, again, theoretically give you the same numbers as before, but it
may be better conditioned numerically.
Actually _finding_ N, or giving you advise on how to do so, is beyond
my powers -- but maybe this will set you on a better road.
--
Tim Wescott
www.wescottdesign.com
Control & Communications systems, circuit & software design.
Phone: 503.631.7815
Cell: 503.349.8432
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